Before you start looking for a statistical tool you are going to need to provide yourself with some operational definitions – specifically – what is your definition of “good enough” and what is your definition of “mass production”?

For example, if you have some kind of baseline metric/requirement, with respect to what is currently acceptable then the definition of “good enough” is….what – 1% better than the acceptable definition, just equal to the current acceptable definition, within some range around the current acceptable definition, etc.

As for mass production – what kind? 10,000 widgets/minute, one widget/fortnight, etc.

I would go with a process capability study. Run the machine for a decent number of parts (~ 50) to get a sense for the inherent variability in the new machine. It is important to recognize that the variation in output will increase over time as you add new lots of raw materials, new operators, etc.